Problem: Reduce to lowest terms: $- \dfrac{8}{3} \div - \dfrac{9}{8} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{9}{8}$ is $- \dfrac{8}{9}$ Therefore: $ - \dfrac{8}{3} \div - \dfrac{9}{8} = - \dfrac{8}{3} \times - \dfrac{8}{9} $ $ \phantom{- \dfrac{8}{3} \times - \dfrac{8}{9}} = \dfrac{-8 \times -8}{3 \times 9} $ $ \phantom{- \dfrac{8}{3} \times - \dfrac{8}{9}} = \dfrac{64}{27} $